Lower bounds for $\text{GL}_2(\mathbb{F}_\ell)$ number fields
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916355872129024 |
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| author | Cristante, Vittoria |
| author_facet | Cristante, Vittoria |
| contents | Let $\mathcal{F}_n(X;G)$ denote the set of number fields of degree $n$ with absolute discriminant no larger than $X$ and Galois group $G$. This set is known to be finite for any finite permutation group $G$ and $X \geq 1$. In this paper, we give a lower bound for the cases $G=\text{GL}_2(\mathbb{F}_\ell), \; \text{PGL}_2(\mathbb{F}_\ell)$ for primes $\ell \geq 13$. We also provide a method to compute lower bounds for any permutation representations of these groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_07029 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lower bounds for $\text{GL}_2(\mathbb{F}_\ell)$ number fields Cristante, Vittoria Number Theory Let $\mathcal{F}_n(X;G)$ denote the set of number fields of degree $n$ with absolute discriminant no larger than $X$ and Galois group $G$. This set is known to be finite for any finite permutation group $G$ and $X \geq 1$. In this paper, we give a lower bound for the cases $G=\text{GL}_2(\mathbb{F}_\ell), \; \text{PGL}_2(\mathbb{F}_\ell)$ for primes $\ell \geq 13$. We also provide a method to compute lower bounds for any permutation representations of these groups. |
| title | Lower bounds for $\text{GL}_2(\mathbb{F}_\ell)$ number fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2408.07029 |